Mathematics

Part of a mathematical formula is written in beige over a blurred image of a dark and light room.

Why major in Mathematics?

Students major in mathematics for many reasons: some are drawn by the beauty of the subject, others by its practicality, and many by a combination of the two. Mathematics provides outstanding training for the mind and develops skills in logical reasoning and problem solving. It plays a central role in science, technology, economics, and data-driven fields, from climate modeling and genomics to finance and medicine. Long the language of physics, mathematics is an essential component of nearly all the sciences, especially in an era of computation and modeling. An undergraduate degree in mathematics opens the door to a wide range of careers and to graduate study in mathematics and many related disciplines.

Mathematics is both a discipline in its own right and a vital language for science, technology, and social inquiry. The Department of Mathematics is committed to teaching mathematics as a creative, rigorous, and evolving field. Through majors that range from theoretical to applied and interdisciplinary, we prepare students for advanced study and for applying mathematical thinking across a broad spectrum of professions.

Courses Recommended for First-Year Students

These courses offer first-year students intending to major in mathematics multiple entry points into the discipline, accommodating different backgrounds and interests. The calculus sequence (UN1101–UN1202), together with Accelerated Multivariable Calculus (UN1205), develops core computational skills and geometric intuition, providing essential tools for understanding functions, rates of change, and multivariable phenomena.

Honors Mathematics A–B (UN1207–UN1208) provides a more theoretical and concept-driven introduction for students seeking an early challenge, while Introduction to Higher Mathematics (UN2000) supports the transition from calculation-based courses to abstract reasoning, logical structure, and proof.

Linear Algebra (UN2010) introduces key ideas such as vector spaces, linear transformations, and matrices, giving students tools that appear throughout mathematics and in many applied fields, including data science, economics, physics, and computer science.

Perspectives in Mathematics (BC2001) is a one-credit, broadly accessible course requiring no prerequisites beyond curiosity and a love of mathematics. Through examples drawn from diverse applications, it offers students an early glimpse of the scope, creativity, and impact of mathematical thinking.

Please check the online catalogue for a description of suggested sequences for the different majors.
 

Our Faculty

Photo of Professor Marco Castronovo

Marco Castronovo

Assistant Professor of Mathematics

Daniela De Silva

Olin Professor of Mathematics, Chair of the Department of Mathematics
Department Chair
Photo of Prof. Alisa Knizel wearing a blue hair and showing her long blond hair.

Alisa Knizel

Assistant Professor of Mathematics
Photo of Prof. Dusa McDuff

Dusa McDuff

Joan Lyttle Birman ’48 Professor of Mathematics

Lindsay Piechnik

Lecturer of Mathematics

Semon Rezchikov

Assistant Professor of Mathematics

Our Department

Catherine Cook

Departmental Administrator

Professor Emeriti

Dave Bayer

Professor Emeritus of Mathematics

Joan Birman

Research Professor, Barnard College | Columbia University, Professor Emerita - Affiliated Professor, University of Haifa, Haifa, Israel (photo by Marianne Cooke)

Academic Support

Tutoring
Tutoring Jobs
AWM Columbia Chapter
Undergraduate Research

Columbia and Barnard students are welcome at all tutoring sessions.

FAQ

What is the relationship between the Barnard and the Columbia math departments?
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Barnard does have a distinct math department, though it is very integrated with Columbia’s. This means that you can take your classes with any professor. Generally, there isn’t a noticeable difference between a Barnard vs. Columbia math class. Your biggest connection to Barnard Math is through your advisor, though the Barnard math faculty are all incredible resources for you as well.

Declaring your major.
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Some information about statistics.
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The thesis requirement.
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